Seminar: Matching Supply and Demand for Medical Practices

Title: Matching Supply and Demand for Medical Practices (Panel Management, Controlling Indirect Waiting Times and Dynamic Appointment Scheduling)
Speaker: Dr Anne Zander – Karlsruher Institut fur Technolgie
Date & Time: 3pm, Wednesday 14 March
Location: Room 439-201, Engineering Science, 70 Symonds St, Auckland.


In my talk, I will cover three topics that I consider to be part of the main topic “Matching Supply and Demand for Medical Practices”. In all three cases, we consider a medical practice, e.g., a practice with one general practitioner.

In Panel Management, we consider a patient panel consisting of those patients that visit the physician on a regular basis. The research question is “How to manage the patient panel in order to achieve a balance between supply and demand now and in the future?” We consider the problem dynamically as we take into account that patients of different age visit the physician with varying frequencies. Considering a time capacity for the physician, we build integer linear programs to determine balanced panels, the mix of patients to be included to reach a balanced panel, and to decide about admission for a specific patient request to enter the panel. We test and compare the solutions of those programs using simulation.

Indirect waiting times or access times of patients are an important indicator for the quality of care of a physician. Indirect waiting times are mainly influenced by the panel size, i.e., the number of patients regularly visiting the physician. To study the nature of this influence, we develop an M/D/1/K/N queueing model in which we include now-shows and rescheduling. In contrast to previous work, we assume that panel patients do not make new appointments if they are already waiting. For a given panel size, we calculate the steady state probabilities for the indirect queue length and further aspects such as the effective arrival rate of patients. We compare those results to the outcomes of a simulation and show that the simplifications we used in the analytical model are justified. The queueing model can help physicians to decide on a panel size threshold in order to maintain a predefined service level with respect to indirect waiting times.

In Dynamic Appointment Scheduling, we want to offer a requesting patient an appointment in real time where we maximize schedule utilization. Hereby, we take different service durations and time preferences of patients into account. We model the problem exactly as a Markov decision process and present a heuristic for realistic problem instances that solves a stochastic ILP. In a simulation, we test and compare the heuristic to simpler strategies.

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